-11+11r(6r+4)=44+10r

Solution for -11+11r(6r+4)=44+10r equation:

-11+11r(6r+4)=44+10r

We move all terms to the left:

-11+11r(6r+4)-(44+10r)=0

We add all the numbers together, and all the variables

11r(6r+4)-(10r+44)-11=0

We multiply parentheses

66r^2+44r-(10r+44)-11=0

We get rid of parentheses

66r^2+44r-10r-44-11=0

We add all the numbers together, and all the variables

66r^2+34r-55=0

a = 66; b = 34; c = -55;
Δ = b2-4ac
Δ = 342-4·66·(-55)
Δ = 15676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15676}=\sqrt{4*3919}=\sqrt{4}*\sqrt{3919}=2\sqrt{3919}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{3919}}{2*66}=\frac{-34-2\sqrt{3919}}{132}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{3919}}{2*66}=\frac{-34+2\sqrt{3919}}{132}
$